Uniqueness Criterion of Stress State of Maxwell Type Viscoelastic Body

Abstract

The paper deals with a criterion of uniqueness between stress state and deformation of a Maxwell type viscoelastic body, of which stress-strain relations are of the Lagrangian form. If the stress state is given, the body force and the surface displacement are uniquely specified by means of generalized Hamilton's principle. Conversely, the uniqueness criterion for the infinitesimal increment of stress of the given infinitesimal variations of body force, surface force and surface displacement, is that a function of the elastic potential and the dissipation function is positive definite.